@Kralc's answer is correct, but to add a little logical-deduction to it...
Let's try to complete the route without passing any cars and see if that is possible. First, exclude all sections of the route that must involve passing a stalled car (marked in red):
Next, without encountering these red sections, draw lines that lead from the entrance and the exit as far as you can go without having to make any decisions about turn-offs (forgive the swerve in the car's path in the top-right of the diagram - I think an animal must have run out in front of me...):
Finally, note that if avoiding red routes and intersections with intermediate parts of the route leading from the entrance, the path of the line drawn from the exit can be forced until it meets the end of the other line:
It is indeed possible to draw a line from the entrance to the exit without encountering a single other car!